The legality of voice recording in the U.S. is governed by laws (Federal
and State) aimed at preventing eavesdropping.
The key legal point, from the perspective of language documentation
projects, is very simple:

Generally, you may record, film, broadcast or
amplify any conversation where all the parties to it
consent. It is always legal to tape or film a
face-to-face interview when your recorder or camera is
in plain view. The consent of all parties is presumed in
these instances.

Note that the laws with respect to video recording are generally more flexible.
As the RCFP page says:

The use of hidden cameras is only covered
by the wiretap
and eavesdropping laws if the camera also records an
audio track. However, a handful of states have adopted
laws specifically banning the use of video and still
cameras where the subject has an expectation of
privacy, although some of the laws are much more
specific. Maryland's law, for example, bans the use of
hidden cameras in bathrooms and dressing rooms.

For recordings made outside the U.S., the applicable law (if any)
will presumably be the law of the place where the recordings are made.
It seems unlikely that there is any place where it is illegal to record
an interaction if all parties consent.

Note that this section only deals with the question of whether it is
legal to make a recording, and not with the question of who owns what aspects
of the result, or whether it is legitimate to distribute or publish
the result.